Ratio between temperature and evapotranspiration

The relationship between temperature and evapotranspiration (ET) is complex and influenced by various environmental factors, but it can often be expressed through empirical correlations or ratios derived from specific studies and models. While there isn't a universal "ratio" between temperature and ET that applies across all contexts, research provides insights into how these two variables interact, often through mathematical relationships or proportional dependencies.

Relationship Overview

Evapotranspiration, the combined process of evaporation from land surfaces and transpiration from plants, is significantly affected by temperature, as it influences the energy available for water vaporization. Higher temperatures generally increase the rate of ET due to greater energy input, which enhances evaporation and plant transpiration, provided other factors like water availability and humidity are not limiting 7. However, this relationship can vary based on whether the environment is energy-limited (where temperature and energy drive ET) or water-limited (where soil moisture availability constrains ET) 6.

Specific Findings on Temperature and ET Correlation

A detailed study conducted in the Sri Songkhram sub-river basin in Thailand using Landsat 5 TM satellite imagery provides a concrete example of the relationship between air temperature and actual evapotranspiration. The research found a polynomial relationship between temperature and daily mean actual ET, with mean air temperature at 296.4 °K (23.4 °C) corresponding to a mean ET of 4.1 mm per day. The relationship is expressed by the equations:

• For temperature in Kelvin: $y = -0.028x^2 + 17.069x - 2593.2$ (R² = 0.987)

• For temperature in Celsius: $y = -0.028x^2 + 1.7608x - 22.932$ (R² = 0.987)
  where $y$ represents actual ET in millimeters, and $x$ is the temperature in the respective unit. This indicates a non-linear relationship where ET increases with temperature up to a certain point before declining, likely due to other limiting factors like humidity or water availability 2.

Energy and Water-Limited Conditions

The relationship between temperature and ET also depends on environmental conditions. In energy-limited settings (common in colder or humid regions), ET and land surface temperature (LST) often show a positive correlation when air temperature is below a threshold for plant transpiration (around 5°C in some studies). Above this threshold, the relationship may become negative due to cooling effects from transpiration. Conversely, in water-limited conditions (common in arid regions), ET and LST typically exhibit a negative relationship, as evaporation and transpiration cool the surface even at lower temperatures 6.

Practical Applications and Ratios

While direct ratios like the "Climate Ratio" (P/Ep, where P is precipitation and Ep is potential evaporation) are used to assess climatic conditions, they do not directly relate temperature to ET but rather contextualize water balance in relation to evaporative demand 1. Temperature's role in ET is often embedded in calculations of potential evapotranspiration (ETo), which can be derived using temperature data alongside other variables like humidity and radiation. For instance, methods to calculate reference evapotranspiration (ETo) incorporate temperature to estimate saturation vapor pressure and its slope, which are critical for determining evaporative demand 34.

In summary, while a direct, universal ratio between temperature and evapotranspiration does not exist, their relationship can be modeled through polynomial equations or contextualized via energy and water availability. The specific correlation depends on local conditions, with temperature serving as a key driver of ET through its influence on energy availability for vaporization. For practical applications, such as irrigation or water management, localized studies like the one in Thailand provide valuable equations to estimate ET from temperature data 2.

Citations:

1. https://gml.noaa.gov/outreach/lesson_plans/Climate%20Ratios.pdf
2. https://www.thaiscience.info/journals/Article/TKJN/10974303.pdf
3. https://www.fao.org/4/x0490e/x0490e08.htm
4. https://www.weap21.org/webhelp/Mabia_Alg_ETRef.htm
5. https://www.fao.org/4/x0490e/x0490e04.htm
6. https://scispace.com/pdf/relationship-between-evapotranspiration-and-land-surface-49d8s971i1.pdf
7. https://en.wikipedia.org/wiki/Evapotranspiration
8. https://pubs.usgs.gov/wri/wri994079/text/evapotranspiration.htm
9. https://www.sciencedirect.com/science/article/pii/S0022169424012216

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